Article pubs.acs.org/JPCC
Ultrafast Carrier Dynamics of Silicon Nanowire Ensembles: The Impact of Geometrical Heterogeneity on Charge Carrier Lifetime Erik M. Grumstrup, Emma M. Cating, Michelle M. Gabriel, Christopher W. Pinion, Joseph D. Christesen, Justin R. Kirschbrown, Ernest L. Vallorz, III, James F. Cahoon,* and John M. Papanikolas* Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-3290, United States S Supporting Information *
ABSTRACT: Ultrafast carrier dynamics in silicon nanowires with average diameters of 40, 50, 60, and 100 nm were studied with transient absorption spectroscopy. After 388 nm photoexcitation near the direct band gap of silicon, broadband spectra from 400 to 800 nm were collected between 200 fs and 1.3 ns. The transient spectra exhibited both absorptive and bleach features that evolved on multiple time scales, reflecting contributions from carrier thermalization and recombination as well as transient shifts of the ground-state absorption spectrum. The initially formed “hot” carriers relaxed to the band edge within the first ∼300 fs, followed by recombination over several hundreds of picoseconds. The charge carrier lifetime progressively decreased with decreasing diameter, a result consistent with a surface-mediated recombination process. Recombination dynamics were quantitatively modeled using the diameter distribution measured from each sample, and this analysis yielded a consistent surface recombination velocity of ∼2 × 104 cm/s across all samples. The results indicate that transient absorption spectroscopy, which interrogates thousands of individual nanostructures simultaneously, can be an accurate probe of material parameters in inhomogeneous semiconductor samples when geometrical differences within the ensemble are properly analyzed.
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INTRODUCTION Methods for the bottom-up synthesis of complex semiconductor nanomaterials have advanced rapidly over the past two decades. Despite efforts to develop uniform and reproducible growth processes, heterogeneity in semiconductor nanostructures is a recurring problem.1,2 The variation from structure-to-structure and synthesis-to-synthesis poses a major challenge for characterization efforts and ultimately to technologies that rely on the identical operation of individual nanoscale objects. For example, small changes in size or morphology of subwavelength or quantum-confined objects can cause pronounced changes in absorption or emission properties.3−8 Similarly, high surface-to-volume ratios cause minor changes in size to strongly influence charge carrier transport and recombination processes.9−11 As a consequence, spectroscopic measurements performed on nanomaterials are fundamentally influenced by structure-to-structure differences and other sources of sample heterogeneity. Techniques that probe ensembles of nanostructures, such as femtosecond transient absorption (TA) spectroscopy, are complicated by experimental observables that reflect the full distribution of nanostructure sizes and shapes as well as extraneous material, including side products, residual reactants, catalysts, etc., that may still remain in the sample. In nanostructures with high aspect ratios, the electronic structure can also be affected by differences in secondary structure (i.e., local curvature in bent wires).12,13 All of these structures, not just the ideal nanostructures, contribute to the signal, producing © 2014 American Chemical Society
nonexponential kinetics that reflect a multitude of dynamical processes. As a result, interpretation of the transient response in terms of simple physical models is often not possible or straightforward. While sample heterogeneity can be partially overcome using ultrafast microscopy methods that interrogate single nanostructures,14−19 they require that data be collected on many individual objects to draw statistically meaningful conclusions. Compared to pump−probe microscopy, TA is easily implemented with a broadband probe, providing a full transient spectrum. The ability to monitor spectral evolution facilitates a detailed analysis, making TA an important tool for characterizing dynamical processes such as carrier relaxation and recombination.12,13 In this paper, we describe the application of TA spectroscopy to the study of carrier dynamics in ensembles of silicon nanowires (NWs). Transient spectra obtained throughout the visible and near-IR (400−800 nm) are composed of a broad photobleach on which narrower features arising from NW absorption and scattering modes appear. The evolution of the spectra with time indicates that the photoexcited carrier population undergoes intraband relaxation to the band edge in several hundred femtoseconds followed by electron−hole recombination in several hundred picoseconds. Examination of NWs of different diameters shows that the recombination Received: January 30, 2014 Revised: March 15, 2014 Published: March 21, 2014 8626
dx.doi.org/10.1021/jp501079b | J. Phys. Chem. C 2014, 118, 8626−8633
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Article
Figure 1. SEM images of NW substrates. (A) Sample grown with 50 nm Au nanoparticles (d50). The dotted circle with a 100 μm diameter illustrates the spatial extent of the pump beam (100 μm fwhm). (B) Magnified image showing a high density of individual NWs. (C) Image showing individual NWs and regions of suboptimal NW growth denoted by arrows.
white light continuum used for the probe beam was generated by focusing ∼3 μJ into a translating CaF2 crystal. The pump was coupled onto a mechanical delay stage, attenuated, and focused onto the sample using a 300 mm lens to achieve a spot size of 100 μm fwhm. The probe was focused onto the sample with a 250 mm aluminum spherical mirror (90 μm fwhm spot size), coupled into a 0.15 m spectrometer dispersed on a 1200 grooves/mm grating, and detected on a high-speed diode array. The pump beam was mechanically chopped at half the repetition rate of the laser (500 Hz), and interleaved pump on and pump off spectra were collected.
process is dominated by a surface-mediated mechanism, in which the average carrier lifetime (τ) is related to the NW diameter (d) and surface recombination velocity (S), i.e., τ = d/ 4S.9,11 The surface recombination velocity provides a measure of surface quality, which is of interest for both fundamental and technological reasons. From a fundamental standpoint, S provides a quantitative means of studying the interaction of carriers with the surface and for comparing different surface passivation strategies. From a technological perspective, S can be related to the density of surface states, which in turn governs the behavior of many active electronic components. Recombination velocities in NWs are often determined using photocurrent methods,5,9,11,20 which require the fabrication of functioning single-NW devices, effectively limiting characterization to a few isolated structures. As an alternative, here we use pump−probe methods to directly time-resolve the carrier lifetime. Using a kinetic model that accounts for the diameter distribution, we extract a value of S for each sample. The recombination velocities are within a factor of 2 of each other across an array of samples with diameters ranging from 30 to 100 nm that were prepared in a similar manner but are generally 2- or 3-fold greater than those obtained at specific points within individual NWs using femtosecond pump−probe microscopy.21 This difference may arise from a number of factors related to the material and structural heterogeneity of the ensemble, underscoring the complexity of interpreting ensemble measurements that probe all materials, desired and undesired, within a sample.
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RESULTS AND DISCUSSION Nanowire Samples. These experiments focus on four samples of NWs, denoted d40, d50, d60, and d100, which were grown using Au catalysts with average diameters of 30, 50, 60, and 100 nm, respectively. Scanning electron microscopy (SEM) images reveal that the NWs remained largely unbroken upon collapse (Figure 1A,B). Imaging of individual structures shows that while the majority of the NWs are smooth (Figure 1C), there are regions of nonuniform growth, as highlighted by the arrows in Figure 1C. These regions result from a number of processes, including the incubation period needed to supersaturate Au catalysts prior to VLS growth22 and from nucleation of multiple NWs from single Au nanoparticles.23 The polydispersity in the NW diameters present in each sample was characterized by measuring the diameters of 150−200 individual NWs in a SEM, resulting in the histogram depicted in Figure 2. The experimental histogram was fit to a Weibull distribution:
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EXPERIMENTAL SECTION Intrinsic Si NW samples were synthesized by a vapor−liquid− solid (VLS) mechanism using Au nanoparticle catalysts.5,17 The reactor was held at 450 °C for 2 min to nucleate wire growth and then cooled (12 °C/min) to 410 °C for continued wire growth over 2 h using 2 sccm SiH4 and 200 sccm H2 at 40 Torr.5 Immersion of the substrate in isopropanol and slow evaporation of the solvent from the surface collapsed the NWs into the dense, randomly oriented mat shown in Figure 1A. The NWs were collapsed to reduce optical scattering and to enhance pump−probe spatial overlap by placing all NWs within the same focal plane. After collapsing the nanowires onto the substrate, they were thermally oxidized at 1000 °C for 1 min under 100 Torr of O2. Transient absorption measurements were performed using pulses centered at 775 nm (150 fs fwhm) derived from a Ti:sapphire regenerative amplifier (Clark-MXR 2210) operating at 1 kHz. The pump beam was generated by frequency doubling 35 μJ of the fundamental in a BBO crystal, and the
k ⎛ d ⎞k − 1 g ′(d) = B⎜ ⎟ e−(d / Γ) ⎝Γ⎠
(1)
Here B is a scaling parameter and k and Γ are parameters that reflect the symmetry and width of the distribution, respectively. A Weibull distribution was used as it is both asymmetric which produces a more accurate representation of the measured diameter distribution and because it has no amplitude at zero diameter. The distributions for the four samples have maxima at 38 nm (d40), 52 nm (d50), 59 nm (d60), and 101 nm (d100) and widths that range from 20 to 40 nm, which presumably arise from a combination of polydispersity in the catalyst diameter and nonuniform NW growth as noted above. While a perfectly uniform diameter along the length of the NW is not expected, no effort was made to measure the diameter of each NW at the same relative position. Thus, the histograms should accurately reflect the distribution of diameters sampled by the TA measurement. 8627
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narrower features that result from optical resonator modes supported within the cross section of the NW.6,7,15,24 While all the samples possess these resonances, the most prominent is observed in the d100 spectrum near 520 nm. Finite-element simulations of the NW absorption spectrum (Figure 3B), obtained by a weighted average of spectra from NWs with diameters ranging from 50 to 150 nm, qualitatively reproduce the absorption profile of the d100 sample. Details of the procedure to generate the simulated spectra are in the Supporting Information. Transient Spectroscopy. Transient absorption (TA) spectra for the four samples are shown in Figure 4 (black solid curves). The spectra were collected at a pump−probe delay of 250 fs using a white light continuum probe that extends from 400 to 800 nm and a pump wavelength of 388 nm (255 μJ/cm2). Pump and probe spot sizes were 100 and 90 μm fwhm, respectively, so the field sampled in these experiments encompassed thousands of wires and was approximately equivalent in size to the circle shown in Figure 1A. Excitation at 388 nm produces carriers with energy near the direct band gap, and given the extinction coefficient of bulk Si (0.02 nm−1),25 we estimate the initial photoexcited carrier density at this fluence to be ∼5 × 1019 cm−3. Because the diameters of the NWs studied are much larger than the Bohr radius (2.2 nm),2 photoexcitation produces free carriers (i.e., bulk-like behavior). The transient spectra for the three smallest diameters are qualitatively similar; each exhibits a broad positive band that spans much of the visible spectrum. For the 100 nm NWs, the broad positive band is accompanied by a narrower derivativelike feature that coincides with the optical resonator mode at ∼520 nm in the ground-state spectrum (Figure 3A). The positive-going signals correspond to a pump-induced increase in the probe intensity (i.e., a photoinduced bleach) that has several potential contributions. The first stems from changes in the absorptive properties of the NW due to band filling by photoexcited free carriers that occupy low-energy states in the conduction and valence bands of Si. Photoinduced absorption by free carriers and trapped carriers may also contribute to the overall transient spectra as a negative-going signal; however, consistent with previous studies of silicon, the overall signal is positive at early times, suggesting that carrier absorption (free or trapped) is a minor component.26−29 In addition, photogenerated carriers decrease the index of refraction, which in turn can reduce the NW scattering and lead to an increase in the probe intensity.20,24 While both optically induced changes in absorption and refractive index have analogous processes in bulk semiconductors, the subwavelength dimensions of the NW give rise to optical resonator modes that can also influence both NW absorption and scattering. For example, photoinduced changes to the refractive index resulting from the presence of free carriers will also shift the position of the NW’s optical resonator modes, which could be the origin of the derivativelike feature seen in the transient spectrum of d100 (Figure 4D). In this scenario, the transient spectrum can be modeled simply by calculating difference spectra, JΔ(λ), according to
Figure 2. Distribution of NW diameters measured by SEM. Histograms were generated by binning the measured diameters in 3 nm increments. Uncertainty in an individual diameter measurement is estimated to be ±5 nm based on making repeated measurements of the same NW. The experimental histogram is fit to a Weibull distribution (eq 1) as shown by the black solid line in each panel.
Ground-State Spectroscopy. Figure 3A shows the UV− vis extinction spectra of the four samples, which are measured in transmission mode and therefore reflect a combination of both absorption and scattering by the NWs. The spectra consist of a broad absorption band that increases toward shorter wavelengths, similar to bulk silicon, superimposed with several
JΔ(λ) =
Figure 3. (A) Measured ground-state extinction spectra (1 − I/I0) of the four diameter NW samples: d40 (black), d50 (red), d60 (blue), and d100 (green). (B) Spectra showing simulated absorption efficiency for an ensemble of NWs weighted by the fits to the distributions shown in Figure 2.
T GS(λ + Δλ) − T GS(λ) T GS(λ)
(2)
where TGS(λ) is the ground-state transmission spectrum and Δλ is a spectral shift. In microcavities, the wavelength supported by an optical resonator mode is proportional to 8628
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Figure 4. Early time (Δt = 275 fs) transient absorption spectra for samples (A) d40, (B) d50, (C) d60, and (D) d100 nm. Black solid lines represent experimental data, and blue dashed lines represent the difference spectra, JΔ, obtained by shifting the ground-state transmission spectrum according to eqs 2 and 3. The agreement between the difference spectrum and the transient spectrum is good in the case of d100 (panel D), especially between 450 and 600 nm. The agreement is not as good at wavelengths longer than 600 nm in any of the samples, consistent with the assignment of this broad feature to band filling and scattering.
the index of refraction,7 suggesting that Δλ = c0Δn, where c0 is a constant scaling factor that is related to the size of the resonator and the mode number. The change in the index of refraction (Δn) depends upon the density of photogenerated carriers (N) and is given by20,22 Δn(λ) = −
λ 2 e 2N 2πn0(λ)c 2m*
at longer wavelengths the transient spectra are likely dominated by band filling and scattering. Although it is difficult to disentangle the relative magnitudes of the contributions due to band-filling, scattering, and changes in the resonator modes, they all scale with the density of photoexcited carriers. Thus, the transient absorption signal reflects the free carrier population and can be used to monitor its decay. Spectral Evolution and Carrier Recombination. The spectral evolution of the 50 nm sample obtained with low pump pulse energies (255 μJ/cm2) is shown in Figure 5. The set of transient spectra show a broad positive-going bleach at early times. The majority of the bleach (∼70%) appears within the instrument response, while the remaining 30% grows in during the first 1 ps with a rise time of 300 ± 40 fs (Figure 5B). We attribute this increase in bleach amplitude to intraband relaxation of the carriers. Photoexcitation at 388 nm (3.2 eV) produces free carriers with ∼2 eV of excess energy relative to the Si band gap (1.12 eV). As the carriers undergo intraband relaxation through phonon scattering, they fill states near the band edges, reducing absorption at visible and near-IR wavelengths. The 300 fs time constant is consistent with previously reported time scales for carrier thermalization in bulk26 and nanocrystalline silicon.30 After the initial growth in the first 1 ps, the amplitude of the broad signal from ∼500−800 nm decays and changes sign around 200 ps, switching from a positive-going bleach signal to a negative-going absorptive signal that persists for more than a nanosecond (see Figure 5A,C). We attribute the decay of the bleach to a reduction in the free carrier population as a result of electron−hole recombination. Multiple recombination mechanisms are potentially present in these NWs, resulting in an apparent recombination rate (k) that is a sum of the rates of all processes, i.e.
(3)
where e is the fundamental charge, n0(λ) is the refractive index in the absence of photoexcited carriers, c is the speed of light, and m* is the reduced mass of the electron and hole (0.2me). The difference spectrum, JΔ(λ), calculated using eqs 2 and 3 is depicted for d100 in Figure 4D (blue dashed curve) and corresponds to a 0.8 nm blue-shift of the ground-state transmission spectrum at 400 nm and a 4.9 nm blue-shift at 800 nm. This spectrum is in qualitative agreement with the transient absorption spectrum observed at 275 fs, largely reproducing the derivative feature, suggesting that the derivative line shape and its subsequent evolution can be understood as a transient spectral shift of the NW ground-state absorption spectrum in response to the photoexcited carrier population. The optical resonator mode in the 100 nm NWs leads to an especially dramatic modulation of the transient spectrum. On the other hand, the smaller diameter NWs do not show distinct optical modes nor the clear derivative-like spectral features in their transient spectra. While the difference spectra, JΔn, calculated for the other three samples (with the same scaling factor, c0) (Figure 4A−C) share some of the features observed in the transient spectra, the overall agreement is not as good as for d100. These results suggests that the early time transient spectra are composed of features from both band filling/ scattering as well as from a transient shifts of the optical resonator modes. It further suggests that the contribution from spectral shifting is largely restricted to the shorter wavelengths (
